3a. 1, 2, 3, or 4 cases b. ^ = 16|, but you cannot
walk | of a dog. If you round down to 16, you will only
make $72. So round up to 17.- x < 2 *■ i i ©— i--------- 1 - 1 —
0 1 2 3 4 5
Lesso n Ch eck 1. D 2. B 3. A 4. C 5a. Multiplication
by -2 ; it is the inverse of division by -2. b. Addition of
4; it is the inverse of subtraction of 4. c. Division by - 6 ;
it is the inverse of multiplication by -6. 6. The inequality
symbol was not reversed when multiplying by a negative.
—5 ( —f) < -5(2), n < —10
Ex er ci ses - x> -10
- p < 32 -
-12 -1 0 - 8 - 6 - 4 - 2
I I 0 I— I— I— I-(^28 3032 3436)
- v< -3 i-
-5 -4 -3 -2 -1 - x> -3
- m<0 -
-5 -4 -3 -2 -1
-I— I— I-
2 - 1- m<2
- m>2
21.c>6
8 10- z> -3
-5 -4 -3 -2 -1 - b :
1 1 - h> -13
-15 -14 -13 -12 -11 -10 - q < 9
6 7 8 9 10 - no more than 66 text messages 33-35. Answers
may vary. Samples are given. 33. -5, -4, -3, -2 - -6, -5, -4, -3 37. Multiply each side by - 4 and
reverse the inequality symbol. 39. Divide each side by 5. - -2 43. 4 45. Sometimes true; sample: It is true
when x = 4 and y = 0.5 but false when x = 4 and
y = -2. 47. Sometimes true; sample: It is true when
x = 4 and y = 2 but false when x = 0 and y = 2. - at least 0.08 mi per min
- 3(-1)>3(§)
-3 >t - 2(0.5) < 2 (lc )
1 < c- 5(f) <5(—2)
n< -10
Mult. Prop, of Ineq.
Simplify.
Mult. Prop, of Ineq.
Simplify.
Mult. Prop, of Ineq.
Simplify.- -^(1) > (_ f s) Mult. Prop, of Ineq.
— 5 > s Simplify. - If the most expensive sandwiches and drinks are
ordered, the cost is 3(7) + 3(2) = 27, leaving $3. If the
most expensive snack is bought, the least number of
snacks you can afford is 1. If the least expensive
sandwiches and drinks are ordered, the cost is
3(4) + 3(1) = 15, leaving $15. If the least expensive snack
is bought, the greatest number of snacks you can afford is
- x < 20, x < 30, x < 40,... ; any inequality
following the one that a is a solution to. This is because
each following inequality has the same solutions as the
previous inequalities, with more values as solutions.
- x < 20, x < 30, x < 40,... ; any inequality
- 3.14d> 29.5 and d > 9.4, so the men's basketballs
need a 10-in. box; 3.14d> 27.75, d> 8.8 so the youth
basketballs need a 9-in. box. 65. D 67. w = € — 3,
18 = 2€ + 2(€ - 3), 18 = 4€ - 6 , 24 = 4€, so € = 6
(Length is 6 in.). 68. x<-11 69. y > 13.6 70. g<5 - —| > c 72. - 1 < b 73. y<75 74.2 75. -2
- 1
Lesso n 3-4 pp. 186-192
Go t I t? 1a. 3 2 - 4 b. n < 3 c. x < 25 2. any width
greater than 0 ft and less than or equal to 6 ft 3. m < -3
4a. b > 3 b. Answers may vary. Sample: adding 1 to
each side. This would gather the constant terms onto one
side of the inequality. 5a. no solution b. all real numbers
Lesso n Ch eck 1. a > 2 2. f < 5 3. z< 13 4. no
solution 5. greater than 0 cm and less than or equal to
8 cm 6. The variable terms cancel each other out and a
false inequality results. 7. Yes; each side can be divided by
2 first. 8. No; there is no solution, since -6 is not greater
than itself. If the inequality symbol were >, your friend
would be correct.
Ex e r c i se s 9. f< 3 11.y> -2 13. r>3.5 - 5s> 250;s> 50 mph 17. k> 1 19. y < - 1
- z<9 23. x< 3 25. f< 6 27. m> -5 29. all
real numbers 31. all real numbers 33. all real numbers - x> -4 37. f> | 39. n > -2 41. a >0 .5
- k:^13 45. 5.5 h 47. D 49a. v> 4 b. 4 < v
c. They are equivalent, d. Check students' work. 51. at
least $3750 53. 3y was subtracted from instead of added
to each side; 7y< 2, y <y. 55. -5, -4, -3, -2, -1,0,
1, 2, 3, 4, 5, and 6 57a. 73 boxes b. 4 trips
Lesson 3-5 pp. 194-199
Go t It? 1. N= {2, 4, 6, 8, 10, 12}; N= {x|x is
an even natural number, x < 12} 2. {n|n < -3 }
3a. {} or 0, {a}, {b}, {a, b}; { } or 0, {a}, {b}, {c},
{a, b}, {a, c}, {b, c}, {a, b, c} b. Yes; every element
of set A is part of set B, since -3 < 0. 4. A' = {February,
April, June, September, November}
I Select ed Answ ers 871